Eight less than a number

Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

Phantasy [73]

Answer:

Part A

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the given values we get;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

$a = R \cdot cos \left(\dfrac{\pi}{n} \right)$

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the values gives;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore, we get;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

5 0

3 years ago

8. a number increased by five and then divided by two

Butoxors [25]

Answer:3

Step-by-step explanation:

1+5=6

6/2=3

4 0

3 years ago

Read 2 more answers

The diagram shows an empty cylindrical container. Ana puts a solid cube of side length 8 cm into the container. She then pours 1

marshall27 [118]

Answer:

<h3><u>Cylinder</u></h3>

$\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}$

Given:

r = 6 cm

h = 18 cm

$\begin{aligned}\implies \sf V &= \sf \pi (6)^2(18)\\& = \sf 648 \pi \: cm^3\end{aligned}$

$\textsf{Volume of a cube}=\sf x^3\quad\textsf{(where x is the side length)}$

Given:

x = 8 cm

$\begin{aligned}\implies \sf V &= 8^3\\& = \sf 512 \: cm^3\end{aligned}$

<h3><u>Volume available to be filled with water</u></h3>

Volume of cylinder - volume of cube

= 684π - 512

= 1532.75204 cm³

1 litre = 1000 cm³

⇒ 1.5 litres = 1000 × 1.5 = 1500 cm³

As 1500 < 1532.75204, the volume of water poured into the container is smaller than the empty space available in the cylinder. Therefore, the water will <u>not</u> come over the top of the container.

4 0

2 years ago

Find the area of shaded region.

Rudiy27

Hey there mate ;),

Area of The shades region is <u>3098 m^2</u>

The solution is attached as picture. Please check.

<em>Answered</em><em> </em><em>by</em><em> </em><em>Benjemin</em>